Unipotent differential algebraic groups as parameterized differential Galois groups

We deal with aspects of the direct and inverse problems in parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (LDAG) G is a PPV Galois group over these fields if and only if G contains a Kolchin-dense finitely generated group. We sh...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2013-07
Main Authors: Minchenko, Andrey, Ovchinnikov, Alexey, Singer, Michael F
Format: Article
Language:English
Subjects:
Algebra
Differential equations
Group theory
Inverse problems
Parameterization
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We deal with aspects of the direct and inverse problems in parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (LDAG) G is a PPV Galois group over these fields if and only if G contains a Kolchin-dense finitely generated group. We show that, for a class of LDAGs G, including unipotent groups, G is such a group if and only if it has differential type 0. We give a procedure to determine if a parameterized linear differential equation has a PPV Galois group in this class and show how one can calculate the PPV Galois group of a parameterized linear differential equation if its Galois group has differential type 0.
ISSN:2331-8422
DOI:10.48550/arxiv.1301.0092